JPEG (and many image/video coding algorithms) are really made up of a couple pieces -- transform, modeling and entropy coding. In the case of JPEG, the transfo

JPEG (and many image/video coding algorithms) are really made up of a couple pieces -- transform, modeling and entropy coding. In the case of JPEG, the transform is handled through breaking the image up into eight by eight blocks that are then run through the DCT and quantized. This is where the loss comes from. Modeling and entropy coding are handled on the coefficients generated above. However, this is done on each 8x8 block (note, I am making a slight simplification ignoring the use of differential compression on the DC coefficients between blocks. Since the algorithm is relegated to encoding at most 64 coefficients at a time, there isn't much "modeling" that can be done. If one reorders the coefficients of the 8x8 blocks to resemble a non-block based transform -- you can perform better modeling to get much better compression with the exact same image quality as the original JPEG image. However, in this case, you lose compatibility with a JPEG encoder since the format of the coefficients is not JPEG.